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hay, another app engine experiment is born…

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0 parents commit 53f2edda78ee724650981fe18979b281cd42ed07 Attila Oláh committed Mar 27, 2013
Showing with 419 additions and 0 deletions.
  1. +1 −0 api/__init__.py
  2. +75 −0 api/batch.py
  3. +32 −0 api/ds.py
  4. +21 −0 app.yaml
  5. +1 −0 prcert/__init__.py
  6. +1 −0 prcert/_small_primes.py
  7. +59 −0 prcert/compress.py
  8. +52 −0 prcert/mesq.py
  9. +8 −0 prcert/small_primes.py
  10. +58 −0 prcert/varint.py
  11. +111 −0 prcert/verify.py
1 api/__init__.py
@@ -0,0 +1 @@
+# -*- coding: utf-8 -*-
75 api/batch.py
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+# -*- coding: utf-8 -*-
+
+from google.appengine.api import files
+from google.appengine.ext import blobstore
+from google.appengine.ext import ndb
+from google.appengine.ext import webapp
+from google.appengine.ext.webapp import blobstore_handlers
+
+from prcert import compress
+from prcert import verify
+
+from . import ds
+
+
+class Batch(blobstore_handlers.BlobstoreDownloadHandler):
+ """Batch download handler."""
+
+ @ndb.synctasklet
+ def get(self, batch_hash, suffix=''):
+ """Redirect to the batch of certs, if available."""
+ key = ds.batch_key(batch_hash)
+ entity = yield key.get_async()
+ if entity is None:
+ # Batch not found:
+ self.response.out.write(u'Batch not found.')
+ self.response.status = 404
+ raise ndb.Return()
+ if suffix == 'bz2':
+ # BZ2-compressed data was requested, let the blobstore handle it:
+ self.send_blob(blobstore.BlobInfo(entity.blob))
+ raise ndb.Return()
+ batch_data = entity.read()
+ if suffix:
+ batch_data = compress.compress(batch_data, algorithm=suffix)
+ self.response.content_type = b'application/octet-stream'
+ self.response.out.write(batch_data)
+
+
+class BatchUpload(Batch):
+ """Batch upload handler."""
+
+ @ndb.synctasklet
+ def put(self, batch_hash):
+ """Verify and store a batch of certs."""
+ key = ds.batch_key(batch_hash)
+ entity = yield key.get_async()
+ data = self.request.body
+ if entity is not None:
+ self.response.out.write(u'A batch with the same name exists, try patching!')
+ self.response.content_type = 'text/plain'
+ self.response.status = 409
+ raise ndb.Return()
+ data = verify.batch(data, batch_hash, recompress=True)
+ if not data:
+ self.response.out.write(u'Verification failed!')
+ self.response.content_type = b'text/plain'
+ self.response.status = 400
+ raise ndb.Return()
+ # Store the data in the blob store:
+ blob_name = files.blobstore.create(mime_type=b'application/octet-stream')
+ with files.open(blob_name, b'ab') as blob:
+ blob.write(self.request.body)
+ files.finalize(blob_name)
+ # Store a reference to the blob in the datastore:
+ new_batch = ds.Batch(key=key, blob=files.blobstore.get_blob_key(blob_name))
+ self.response.out.write(u'Batch accepted!')
+ self.response.content_type = b'text/plain'
+ self.response.status = 202
+ yield new_batch.put_async()
+
+
+app = webapp.WSGIApplication([
+ (r'^/batch/([0-9a-f]+)$', BatchUpload),
+ (r'^/batch/([0-9a-f]+)(?:.(bz2|gz|z))?$', Batch),
+])
32 api/ds.py
@@ -0,0 +1,32 @@
+# -*- coding: utf-8 -*-
+
+import bz2
+
+from google.appengine.ext import blobstore
+from google.appengine.ext import ndb
+
+
+COMPRESS = True
+
+
+class Batch(ndb.Model):
+ """A NULL-separated list of certificates of a growing list of primes."""
+
+ blob = ndb.BlobKeyProperty(required=True, indexed=False)
+
+ def open(self, *args, **kw):
+ """Open a BlobReader instance for reading the blob."""
+ return blobstore.BlobInfo(self.blob).open(*args, **kw)
+
+ def read(self, decompress=True):
+ """Read the contents of the blob."""
+ with self.open() as blob:
+ data = blob.read()
+ if decompress:
+ data = bz2.decompress(data)
+ return data
+
+
+def batch_key(batch_hash):
+ """Generate a batch key."""
+ return ndb.Key('Batch', batch_hash)
21 app.yaml
@@ -0,0 +1,21 @@
+application: prattcerts
+version: 1
+runtime: python27
+api_version: 1
+threadsafe: false
+
+
+builtins:
+- remote_api: on
+
+
+libraries:
+- name: webapp2
+ version: "2.5.2"
+- name: webob
+ version: "1.2.3"
+
+
+handlers:
+- url: /batch/(?:[a-z0-9]+)(?:.(?:bz2|gz|z))?
+ script: api.batch.app
1 prcert/__init__.py
@@ -0,0 +1 @@
+# -*- coding: utf-8 -*-
1 prcert/_small_primes.py
@@ -0,0 +1 @@
+SMALL_PRIMES = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997, 1009, 1013, 1019, 1021, 1031, 1033, 1039, 1049, 1051, 1061, 1063, 1069, 1087, 1091, 1093, 1097, 1103, 1109, 1117, 1123, 1129, 1151, 1153, 1163, 1171, 1181, 1187, 1193, 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59 prcert/compress.py
@@ -0,0 +1,59 @@
+# -*- coding: utf-8 -*-
+
+import bz2
+import gzip
+import zlib
+
+try:
+ import cStringIO
+ _StringIO = cStringIO.StringIO
+except ImportError:
+ import StringIO
+ _StringIO = StringIO.StringIO
+
+
+AVAILABLE_ALGORITHMS = b'bz2', b'gz', b'z'
+
+DEFAULT_ALGORITHM = AVAILABLE_ALGORITHMS[0]
+
+
+def _gzip(data):
+ """Compress using gzip."""
+ return gzip.GzipFile(fileobj=_StringIO(data), mode=b'rb').read()
+
+
+def _gunzip(data):
+ """Decompress using gzip."""
+ buff = _StringIO()
+ gzip.GzipFile(fileobj=buff, mode=b'wb').write(data)
+ buff.seek(0)
+ return buff.read()
+
+
+def compress(data, algorithm=b'bz2'):
+ """Compress the data using the given algorithm."""
+ if algorithm == b'bz2':
+ return bz2.compress(data)
+ if algorithm == b'gz':
+ return _gunzip(data)
+ if algorithm == b'z':
+ return zlib.compress(data)
+ raise ValueError(u'Compression algorithm must be one of {!r}, not {!r}.'.format(AVAILABLE_ALGORITHMS, algorithm))
+
+
+
+def decompress(data):
+ """Try to decompress the data."""
+ try:
+ return bz2.decompress(data)
+ except IOError:
+ pass
+ try:
+ return _gunzip(data)
+ except IOError:
+ pass
+ try:
+ return zlib.decompress(data)
+ except zlib.error:
+ pass
+ return data
52 prcert/mesq.py
@@ -0,0 +1,52 @@
+"""Modular exponentiation by squaring."""
+
+import sys
+
+
+try:
+ __range = xrange
+except NameError:
+ __range = range # Python 3+
+
+
+def mesq(base, exp, mod, debug=False):
+ """Modular exponentiation by squaring."""
+ if debug:
+ # Print some debugging output. Don't use with huge numbers!
+ print('({}**{})%{} ='.format(base, exp, mod))
+ print('(({}%{})**{})%{} ='.format(base, mod, exp, mod))
+ log, cexp = '', 1
+ for x in reversed('{:b}'.format(exp)):
+ if x == '1':
+ log = '*((({}%{})**{})%{})'.format(base, mod, cexp, mod) + log
+ cexp *= 2
+ print('({})%{} ='.format(log[1:], mod))
+ log, nexp = '', 0
+ for x in reversed('{:b}'.format(exp)):
+ if x == '1':
+ args = '('*nexp*2, base, mod, '**2)%{})'.format(mod)*nexp
+ log = '*{}({}%{}){}'.format(*args) + log
+ nexp += 1
+ print('({})%{} ='.format(log[1:], mod))
+ # Loop until we have the result:
+ result, counter = 1, 0
+ cache = (counter, base % mod)
+ while exp:
+ leap = 1
+ if exp & 1:
+ current = cache[1]
+ for x in __range(counter - cache[0]):
+ current = pow(current, 2) % mod # pow() is fast!
+ cache = (counter, current)
+ result = (result * current) % mod
+ else:
+ # In case of many zeros, this will give a small speedup:
+ while not exp & ((1<<(leap*2))-1):
+ leap *= 2
+ counter += leap
+ exp >>= leap
+ return result
+
+
+if __name__ == '__main__':
+ print(mesq(*(int(x) for x in sys.argv[1:4]), debug=False))
8 prcert/small_primes.py
@@ -0,0 +1,8 @@
+# -*- coding: utf-8 -*-
+
+from ._small_primes import SMALL_PRIMES
+
+
+def is_small_prime(n):
+ """Check if a number is a small prime."""
+ return n in SMALL_PRIMES
58 prcert/varint.py
@@ -0,0 +1,58 @@
+# -*- coding: utf-8 -*-
+"""Base 128 (little-endian) varint encoding & decoding."""
+
+
+def uencode(uint):
+ """Encode to an unsigned varint."""
+ group = uint & 0x7f
+ uint >>= 7
+ result = chr((uint and 0x80 or 0x00)|group)
+ while uint:
+ group = uint & 0x7f
+ uint >>= 7
+ result += chr((uint and 0x80 or 0x00)|group)
+ return result
+
+
+def _udecode_pos(raw):
+ """Decode an unsigned varint (and return cursor position)."""
+ char = ord(raw[0])
+ pos, result = 1, char & 0x7f
+ if char & 0x80:
+ for i, char in enumerate(raw[1:], 1):
+ char = ord(char)
+ result |= (char & 0x7f) << (i*7)
+ if not char & 0x80:
+ pos += i
+ break
+ return result, pos
+
+
+def udecode(raw):
+ """Decode an unsigned varint."""
+ return _udecode_pos(raw)[0]
+
+
+def udecode_all(raw):
+ """Decode a list of unsigned varints."""
+ while raw:
+ uint, pos = _udecode_pos(raw)
+ yield uint
+ raw = raw[pos:]
+
+
+def uencode_all(*uints):
+ """Encode a list of unsigned varints."""
+ return ''.join(uencode(uint) for uint in uints)
+
+
+def decode_cert(raw):
+ """Decode a certificate, returning the certificate and a generator yielding pairs."""
+ parts = udecode_all(raw)
+ return parts.next(), tuple(_pairs(parts))
+
+
+def _pairs(parts):
+ """Pair the results of a generator."""
+ while True:
+ yield parts.next(), parts.next()
111 prcert/verify.py
@@ -0,0 +1,111 @@
+# -*- coding: utf-8 -*-
+
+import hashlib
+import math
+
+from . import compress
+from . import mesq
+from . import varint
+from . import small_primes
+
+
+NULL = b'\x00'
+
+BATCH_SIZE = 16
+CYPHER = hashlib.sha1
+
+
+class Error(BaseException):
+ """Verification error."""
+
+
+def _b_hash(prime, b_size=BATCH_SIZE):
+ """Return the batch name for the prime."""
+ return CYPHER(varint.uencode(prime>>b_size)).hexdigest()
+
+
+def _factors(n):
+ """Naive factorization algorithm, but good enough for witnesses."""
+ limit, check, num = int(math.sqrt(n)) + 1, 2, n
+ for check in xrange(2, limit):
+ while not num % check:
+ yield check
+ num //= check
+ if num > 1:
+ yield num
+
+
+def batch(data, b_hash, b_size=BATCH_SIZE, recompress=None):
+ """Verify NULL-separated certificates of a growing list of primes."""
+ # Verify the data:
+ data = compress.decompress(data)
+ if not data:
+ return False
+ # Decode and verify the certificate:
+ current_cert = b''
+ min_prime = max_prime = None
+ current_prime = previous_prime = None
+ for part in data:
+ if part != NULL:
+ current_cert += part
+ else:
+ previous_prime, current_prime = current_prime, cert(current_cert)
+ if not current_prime:
+ return False
+ if current_prime <= previous_prime:
+ return False
+ if min_prime is None:
+ min_prime = current_prime
+ else:
+ min_prime = min(min_prime, current_prime)
+ if max_prime is None:
+ max_prime = current_prime
+ else:
+ max_prime = max(max_prime, current_prime)
+ current_cert = b''
+ # Make sure the batch size is not too large:
+ if min_prime>>b_size != max_prime>>b_size:
+ return False
+ # Make sure the batch name is correct:
+ if _b_hash(min_prime, b_size) != b_hash:
+ return False
+ # Looks like the batch is valid.
+ if recompress:
+ if recompress is True:
+ recompress = compress.DEFAULT_ALGORITHM
+ data = compress.compress(data, algorithm=recompress)
+ return data
+
+
+def cert(data):
+ """Verify a single certificate."""
+ # Smoke test:
+ counter = 0
+ for part in data:
+ if not ord(part) & 0x80:
+ counter += 1
+ if not counter % 2:
+ return False
+ # Unpack the certificate:
+ product = 1
+ witness, pairs = varint.decode_cert(data)
+ for factor, exp in pairs:
+ product *= pow(factor, exp)
+ prime = product + 1
+ # Verify the certificate:
+ for factor, exp in pairs:
+ if mesq.mesq(witness, product/factor, prime) == 1:
+ return False
+ if mesq.mesq(witness, product, prime) != 1:
+ return False
+ # Test that the witness is coprime to the product:
+ if not small_primes.is_small_prime(witness):
+ # These are the factors of the product:
+ factors = [factor for factor, exp in pairs]
+ for factor in _factors(witness):
+ # If the witness factor is one of the product factors, it does not devide the prime:
+ if factor not in factors:
+ # Otherwise, we have to check:
+ if not factor % prime:
+ return False
+ return prime

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